I think the biggest thing is self-inspection.
You can't always convince yourself that you're ok with something, and thereby force yourself to be ok with it. Sometimes you can (at least, I can) "just decide" it's not going to bother you anymore and, then it doesn't. But that doesn't always work.
You need to look deep inside and see why are you bothered by your partner having other relationships.
Fear is the most common motivator, so that's a good place to start. Or maybe your partner changed their behaviour when they started dating this other person, and that's what you're reacting to.
And maybe it's not "other relationships" in general, but specific other people. Just because you're ok with polyamory and open relationships doesn't mean you like every random person who comes into your life. I don't mean that as support for vetos, but sometimes just acknowledging "you know what, I just really don't like her" can go a long way to accepting that she's there. It changes it from "I don't like you dating someone else" to "I don't like her and I don't want to be around her."
And frankly, some people are just plain hypocritical. I personally don't think there's anything inherently wrong with being hypocritical, as long as you acknowledge it and own it. Of course, you also give up the right to be surprised when your partners react with "fuck that shit" and walk out the door. But at least it's open and honest...
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker